Does Objectivism prove existence is consciousness?

[Some philosophers] claimed that man obtains his knowledge of the world by deducing it exclusively from concepts, which come from inside his head and are not derived from the perception of physical facts (the Rationalists)....

Rationalism, in turn, is also a widespread instance of "Kant's gimmick," which Ayn Rand mentions briefly in the final paragraph of Chapter 6, "Axiomatic Concepts," in Introduction to Objectivist Epistemology:

A man's protestations of loyalty to reason are meaningless as such: "reason" is not an axiomatic, but a complex, derivative concept -- and, particularly since Kant, the philosophical technique of concept stealing, of attempting to negate reason by means of reason, has become a general bromide, a gimmmick worn transparently thin.

Concept stealing, in turn, is discussed briefly in the Lexicon under the topic of "'Stolen Concept,' Fallacy of."

"Information" is a stolen concept in the question under discussion. The question treats it as a well understood "given" (like deductive logic and Aristotle's Law of Non-Contradiction), but if one examines it more closely, one finds that "information," like all of man's knowledge, depends on the axiomatic primary concepts of existence, identity and consciousness. Thus, one cannot logically use "information" to show that existence and/or consciousness are not what they are, or that consciousness has primacy over existence.

The expression, "consciousness is identification," comes from Galt's speech in Atlas Shrugged:

To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was—no matter what his errors—the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of his statement. I am here to complete it: Existence is Identity, Consciousness is Identification.

This is not a "definition" of "consciousness." It is a description of what consciousness does. Likewise, "existence is identity" is not a definition of existence. It is a description of what existence contains, not merely the presence of concrete "existents," but also the fact that each one of them is what it is.

Update

Sometimes there can be great value in "dropping a hint" for others to contemplate if they are interested, to serve as a possible springboard for further discussion. Comments by another highly capable Objectivist-Answer provider have taken issue with my treatment of the relation between existence and consciousness generally, and between mind and body in man. Accordingly, I'm happy to elaborate.

It is often assumed that anyone who rejects the idea of a "spiritual dimension" of existence must therefore be a materialist. The spiritual-material dichotomy (also known as the soul-body dichotomy) is widespread in the world today, pervasively and perniciously so. There is a brief selection of Objectivist excerpts on it in The Ayn Rand Lexicon under the topic of "Soul-Body Dichotomy." (Also refer to "Moral-Practical Dichotomy.") Objectivism, however, does not reject "spirituality" entirely; Objectivism actually upholds it strongly, in a specific form. An electronic search for "spiritual" in the literature Objectivism produces 144 topics that refer to it in one form or another, often as criticism of conventional views, but also in some cases as a "spirited" defense of man's "spirit" and the "spiritual dimension" of man's existence.

Ayn Rand was extremely careful to clarify what she meant by "spiritual." In "The Objectivist Ethics" (TOE, Chap. 1 in VOS), in a discussion of the trader principle, Ayn Rand mentions:

In spiritual issues -- (by "spiritual" I mean: "pertaining to man's consciousness") -- the currency or medium of exchange is different, but the principle is the same. Love, friendship, respect, admiration are the emotional response of one man to the virtues of another, the spiritual payment given in exchange for the personal, selfish pleasure which one man derives from the virtues of another man's character.

(Quoted from p. 35 in the Signet paperpack edition of VOS.) A similar passage appears in "Of Living Death" (VOR Chap. 8, p. 54):

It is not against the gross, animal, physicalistic theories or uses of sex that the encyclical [Humanae Vitae (Of Human Life)] is directed, but against the spiritual meaning of sex in man's life. (By "spiritual" I mean pertaining to man's consciousness.) It is not directed against casual, mindless promiscuity, but against romantic love.

And again in connection with "teleological measurement" in Introduction to Objectivist Epistemology, Chap. 4, Ayn Rand observes:

The same kind of measurement [teleological, ranking one thing as greater or less than others in some respect] guides man's actions in the wider realm of moral or spiritual values. (By "spiritual" I mean "pertaining to consciousness." I say "wider" because it is man's hierarchy of values in this realm that determines his hierarchy of values in the material or economic realm.)

In my own discussion of the relation of existence and consciousness (and mind and body), I wanted to highlight Objectivism's recognition of human spirit as well as Objectivism's rejection of a "spiritual dimension" in insentient nature. Objectivists are not "spiritualists" in the conventional sense, but neither are they "materialists" in the conventional sense. In the Objectivist sense, Objectivists are both. Objectivism integrates the material and the spiritual, man's mind and body, as different but closely interrelated aspects of man's existence. Objectivism also very consistently emphasizes that while consciousness is an important fact of existence, it does not have "primacy" over existence; existence has primacy over consciousness. (See "Primacy of Existence vs. Primacy of Consciousness" in the Lexicon.)

One could almost say that Objectivism is "religious" in its view of consciousness -- an exalted, abstract but thoroughly rational view -- as Ayn Rand explains in her Introduction to the 25th Anniversary Edition of The Fountainhead:

Religion's monopoly in the field of ethics has made it extremely difficult to communicate the emotional meaning and connotations of a rational view of life.... it has usurped the highest moral concepts of our language [such as "Exaltation," Worship," "Reverence," and "Sacred"], placing them outside this earth and beyond man's reach....

But such concepts do name actual emotions, even though no supernatural dimension exists; and these emotions are experienced as uplifting or ennobling, without the self-abasement required by religious definitions. What, then, is their source or referent in reality? It is the entire emotional realm of man's dedication to a moral ideal.

By highlighting Objectivism's "spirituality" (properly understood), I seek to bring pause to the typical thought processes of conventional spiritualists who may nevertheless find Ayn Rand's view of the morally ideal in human spirit intriguing, as well as any materialists who may likewise find Ayn Rand's views uplifting or ennobling.

It is certainly a "stretch" to describe existence as conscious, even though existence is abundantly teeming with conscious entities. It is perhaps less of a stretch to describe existence as alive, since it is abundantly teeming with life of countless varieties. I offer these "stretches" as an invitation and challenge to look at existence and see not just rocks and sand and wind and rain, etc., but to see life, everywhere, and conscious entities, too.